Exactly so, that would have made sense rather than what I encountered.It shouldn't be beyond the ability of modern passenger information systems to display the correct information in an unambiguous manner. For example the departure board on the concourse at Waterloo could display Addlestone as the destination, with a footnote saying "train continues to Weybridge". The on board screens could display "Weybridge via Addlestone" (bold for emphasis, but upper-case would work too if that was easier).
Or simply display Addlestone everywhere (both on board & on external destination displays, and on stations) until the train has departed from Clapham Junction- as anyone wanting Weybridge boarding up to that point* would be better off catching a Woking stopper.
*=By which I mean Waterloo, Vauxhall or Clapham Junction. Queenstown Road is an exception if the service calls there, but I can't imagine there's a large number of passengers making that journey who are also completely unfamiliar with the quirks of the former LSWR!
In reality, I already knew so it didn’t matter to me, but I think if it had been advertised along the lines you suggest it would have been better for many.
